A rectangular garden has a length 3 times its width. If the perimeter is 64 meters, what is the area of the garden?

How to Calculate the Area of a Rectangular Garden with a Perimeter of 64 Meters

If you’ve ever been curious about how to find the area of a rectangular garden from its perimeter and a ratio between its length and width, this article is for you. Today, we’ll solve a classic geometry problem: a rectangular garden where the length is three times the width, and the total perimeter is 64 meters. What’s the garden’s area? Let’s break it down step-by-step for clear understanding and practical insight.

Understanding the Context

Understanding the Problem

We know:
- The length \( L \) is 3 times the width \( W \), so:
\( L = 3W \)
- The perimeter \( P \) is 64 meters.
For a rectangle, perimeter formula is:
\( P = 2L + 2W \)

We’ll use these two facts to find \( L \) and \( W \), then compute the area \( A = L \ imes W \).

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Key Insights

Step 1: Substitute and Set Up the Equation

Substitute \( L = 3W \) into the perimeter formula:

\[
P = 2L + 2W = 2(3W) + 2W = 6W + 2W = 8W
\]

Given \( P = 64 \) meters, set up the equation:

\[
8W = 64
\]

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Final Thoughts

Step 2: Solve for Width

Divide both sides by 8:

\[
W = \frac{64}{8} = 8 \ ext{ meters}
\]

Now find the length:

\[
L = 3W = 3 \ imes 8 = 24 \ ext{ meters}
\]

Step 3: Calculate the Area

Use the area formula for a rectangle:

\[
A = L \ imes W = 24 \ imes 8 = 192 \ ext{ square meters}
\]